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The THz optical properties and material structure of pyrolytic boron nitride (PBN), highly oriented pyrolytic boron nitride (HOPBN), and pressed boron nitride powder are investigated by THz time-domain spectroscopy. PBN, HOPBN and powder are confirmed as highly oriented structures; the degree of misalignment of hot-pressed boron nitride is indicated. Suitability of PBN for THz optical applications is discussed.
©2013 Optical Society of America
1. Introduction
Boron Nitride is a III-V compound which, like many others in the series, is expected to have high transparency in the THz band. III-V compounds are non-polar, and therefore do not absorb at THz and sub-THz frequencies unless they possess specific phonon resonances. Examples of THz-transparent III-V compounds include GaP, GaAs, GaN and InP. Unlike those, which are all grown as single-crystals or thin films, BN is manufactured as a ceramic and can be produced in large quantities and machined to the desired shape. As such, it is an attractive candidate for THz optics.
Boron Nitride has three possible morphologies analogous to the polymorphs of carbon [1–3]. Two hexagonal forms exist: one of lower density (2.18 g/cm3) and displaying a layered graphite structure (h-BN); the other of higher density (3.48 g/cm3) and displaying a wurtzite structure (w-BN). A diamond-like form with cubic zinc-blende structure (c-BN) can also be generated under high temperature and pressure. Industrial BN is produced in the hexagonal form. A comprehensive list of BN properties can be found in [1–3].
Hexagonal boron nitride is comprised of (BN)3 rings, with very strong intra-layer bonding and weak van der Waals bonding between layers. The B and N atoms in adjacent layers are aligned above one another and alternate by layer, preventing π-orbital overlap (Fig. 1 ) [4]. This structure explains both the high thermal conductivity and high electrical resistivity of BN, since it permits phonon conduction within layers, while electron localization inhibits electrical conduction. With respect to optical properties, the hexagonal crystal structure gives rise to optical anisotropicity, the resulting birefringence being such that the extraordinary ray lies in the ab-plane and the ordinary ray is aligned with the c-axis.
Hot-pressing methods have been developed to achieve nearly full-density shapes comprised of BN, which are produced by hot pressing submicron, turbostratic BN in the presence of a binder phase under temperatures approaching 2000 °C and pressures up to 2000 psi (14 MPa) [5]. High purity grades of hot pressed BN are also available, with the binder phase leached from the shape after it is generated. In contrast, coatings and layers of pyrolytic boron nitride (PBN) are grown on substrate by chemical vapor deposition techniques at elevated temperatures up to 2000 °C using gaseous sources of boron and nitrogen [6,7]. Highly oriented pyrolytic boron nitride (HOPBN) is produced from PBN by compression-annealing and re-crystallization [7].
In this paper the optical properties and structure of pyrolytic boron nitride (PBN), highly-oriented pyrolytic boron nitride (HOPBN), and pressed BN powder are investigated.
2. Experimental
Samples of fully dense PBN were made by introducing a boron source gas (boron trichloride) and a nitrogen source gas (ammonia) into a reduced pressure chamber at elevated temperatures (~1970 °C), with boron nitride forming as a deposit on a high temperature substrate (graphite). Depending on the flow rates, temperatures, and pressures, three different type structures of PBN can be achieved: a purely turbostratic structure analogous to pyrolytic carbon (Type I), a more crystalline structure with higher density (Type II), and a crystalline structure with a columnar component (Type III) [6]. The form investigated in this study was Type III material. Two of the samples were cut along the c-axis, whilst the third was cut orthogonally to it.
HOPBN was made by first depositing PBN material. It was then compression-annealed under pressures up to 1000 kg/cm2 at temperatures up to 2350 °C. High temperature compression annealing enables recrystallization of pyrolytic boron nitride resulting in growth and orienting of the crystalline domains. The output of this process is a mica-like layered material [8].
Pressed powder samples were made by mixing BN powder with 10 wt% isopropanol and pressing at 100 bar for 60 s. BN powder was comprised of fully dense BN grains with an average size of 45 μm [8]. The porosity of the pressed powder tablet was estimated from its measured weight and volume and the known density of BN (2.18 g/cm3 [1–3]), and was found to be 12%.
The optical properties of boron nitride materials at THz frequencies were studied using a standard type THz time-domain spectrometer described in detail elsewhere [9]. The THz beam in the instrument is linearly polarised, allowing measurements of birefringence by rotating the sample relative to the beam.
3. Pyrolytic boron nitride (PBN)
Figure 2 shows the refractive indices of PBN, and these are also listed in Table 1 . In a previous study [9] several grades of hot-pressed BN were investigated, allowing the refractive indices of fully dense material to be extrapolated, also listed in Table 1. A large discrepancy is evident between the refractive indices of PBN and hot-pressed BN, which requires explanation.
Table 1. Refractive Indices and Loss Coefficients of Different Types of Boron Nitride
The microcrystals of PBN are highly oriented; therefore it may be assumed that the refractive indices measured in PBN are close to the values of no and ne obtaining in a fully dense, single-crystal BN. In contrast, hot-pressed BN grows as platelets approximately aligned with the pressing axis, as depicted schematically in Fig. 3 and shown in the micrograph in Fig. 4 . The crystalline orientation within each platelet is uniform such that the platelet lies in the ab-plane. At the same time, the c-axes of individual platelets adopt a distribution of angles relative to the pressing direction [5,10]. The difference in the refractive indices of PBN and hot-pressed BN then indicates the degree of misalignment of the platelets.
This is due to the fact that a beam traversing a sample containing platelets whose c-axes incline at a variety of angles, as depicted in Fig. 3, will contain both ordinary and extraordinary components, and therefore will experience a mean refractive index containing both no and ne contributions. In performing measurements on hot-pressed BN samples, a beam whose polarization was perpendicular to the pressing axis (Fig. 3) was considered as nominally ordinary, whilst polarization parallel to the pressing axis was considered as nominally extraordinary. However, owing to platelet misalignment, such beams in fact were constituted of both ordinary and extraordinary components.
As noted above the refractive indices of PBN may be interpreted as representing the true values of no and ne; whilst the indices measured in hot-pressed BN (denoted h. p. BN) combine contributions from both no and ne, in proportions related to platelet geometry and orientation. The respective fractional contributions of no and ne that would produce the values observed in hot-pressed BN can be obtained in a straightforward manner from the values of no (PBN), ne (PBN), no (h. p. BN) and ne (h. p. BN), listed in Table 1:
It is notable that the fractional contributions of no and ne are unequal for the nominally ordinary and extraordinary beams. This may be explained by the asymmetry in the transverse and lateral dimensions of the platelets. As the diagram in Fig. 3 shows, platelets grow with their c-axis transverse to their plane. Their shapes are flake-like, such that their thickness (dedge) is much smaller than their lateral dimension (dface), as also seen in the micrograph in Fig. 4. In consequence of the asymmetry between the platelet dimensions along the c-axis and perpendicular to it, the nominally ordinary and the extraordinary beams will experience unequal interactions with platelets in their paths. For the nominally ordinary beam, the interaction length with platelet is its thickness dedge, which is of the order of ~2 μm [5,10]. In contrast, the nominally extraordinary beam interacts through the length of the platelet face dface which is much larger than dedge. As a result, the contribution of ne to the ordinary value measured in hot-pressed BN will be considerably smaller than the contribution of no to the extraordinary value.
The loss coefficients of PBN are shown in Fig. 5 . Notably, the ordinary loss in c-cut material is very low, as expected in fully dense BN. However, the material is seen to be strongly dichroic. More surprisingly, the ordinary loss differs in samples cut perpendicular and parallel to the c-axis.
Fig. 5 Loss coefficients of PBN. Symbols ┴ and || denote samples cut perpendicular to the c-axis (c-cut) and parallel to it. Dotted lines denote fits to Eq. (3); the Ai coefficients are listed in Table 2.
In cases where loss is a featureless rising edge, as seen in Fig. 5, it is not possible to distinguish between loss due to absorption and scattering. Indeed scattering is expected to contribute significantly to loss in any polycrystalline material, and was found to be a major source of loss in hot-pressed BN [9]. Therefore the increased ordinary loss in the sample cut parallel to the c-axis compared to that cut perpendicular to the c-axis may be explained by additional scattering.
The mechanism for such differential scattering can be understood by considering the growth pattern of PBN. Pyrolytic BN is grown on a substrate where it is deposited in parallel layers ~2 μm thick [11], as depicted in Fig. 6 . The layers grow with high crystalline orientation is such that the c-axis lies in the plane of the layer (note that this is different from platelets in hot-pressed BN). The inter-layer boundaries cause a periodic variation in the refractive index, akin to an index grating. In addition to the layered structure, the material contains randomly distributed inclusions originating in the substrate, whose size is of the order of 10 μm [6]. These inclusions are deposited on the surface of the growing material, such that subsequent growth layers are deformed to accommodate them. The layers are oriented parallel to the c-axis, and deformation occurs in a plane orthogonal to it.
As a consequence, a beam traversing a c-cut sample (cut perpendicular to the c-axis) will propagate parallel to the layers, experiencing minimal scattering from inter-layer boundaries. In contrast, the beam traversing a sample cut parallel to the c-axis will encounter a stack of layers interspersed with boundary regions, and thus will suffer scattering from the resulting grating. The ordinary beam will experience scattering from the layers, whilst the extraordinary beam will be scattered by both layers and deformations associated with inclusions. In addition to causing scattering, the inter-layer boundaries may contain material with a high concentration of defects, and therefore charges, which may give rise to conductivity and thus absorption loss.
In order to clarify the loss mechanisms in PBN, the loss curves in Fig. 5 were fitted to the equation
where ν is the frequency. Unweighted least-squares fitting was used, and the obtained coefficients are listed in Table 2 . The factor A4ν4 represents Rayleigh scattering, and was seen to be contributing only to αo║. The factor A2ν2 would be due to the combined amorphous absorption [12] and Mie scattering, but was found to be negligible in all cases. Unexpectedly, the loss was seen to be dominated by the linear factor A1ν1, requiring explanation. In contrast, the loss curve of hot-pressed BN is dominated by the quadratic component, with contribution from the forth-power component, as may be expected in a ceramic material.Since single-crystal BN is expected to be transparent, it may be assumed therefore that the attenuation in PBN is caused by inter-layer boundaries. As noted above, the index variation at the boundaries would produce a form of index grating. Transmissivity of such gratings is inversely proportional to the frequency, explaining the observed linear relationship between attenuation and frequency [13]. The presence of additional forth-power terms indicates Rayleigh scattering, which may be ascribed to inclusions.
C-cut PBN is thus seen as having negligible dispersion and low loss, which makes it suitable for THz optical applications such as windows and lenses, in particular in harsh environments where polymer materials are unsuitable. Compared with silicon, which is commonly used for THz optics, PBN has a lower refractive index (2.3 vs 3.4 [14]) and is less brittle, although its loss is higher [14] and it cannot take optical polish. However, compared with oxide crystals, such as quartz, sapphire and MgO, absorption loss of PBN is lower or comparable and its dispersion much lower [14,15].
4. Highly oriented pyrolytic boron nitride (HOPBN)
HOPBN is a mica-like material which consists of thin, brittle, easily separated layers tens of microns thick [7]. Samples of HOPBN were consequently irregularly-shaped pieces, naturally cleaved, and of varying and non-uniform thicknesses. Measurements on such samples were particularly difficult because their thickness was ill-defined and their surface rough on the scale of the wavelengths used. Moreover, the samples are produced as thin slivers oriented in the ab-plane, so that only the optical constants for the ordinary ray can be measured, whilst those for the extraordinary ray are inaccessible.
The refractive index was evaluated by measuring the frequency-averaged THz optical thickness of multiple samples, obtained from the time-domain data as the delay of the THz peak transmitted through the sample relative to the reference peak. This was then plotted against sample thickness as measured by a micrometer and adjusted for sample density, which varied between 1.98 and 2.21 g/cm3. The slope of the data then gives the mean (frequency-averaged) refractive index, as shown in Fig. 7 . The mean refractive index of HOPBN was found to be 2.30 ± 0.02, which is in agreement with the ordinary refractive index of PBN.
Fig. 7 The frequency-averaged refractive index of HOBN, obtained by plotting the THz optical thickness of the samples against their thickness.
Once the mean ordinary refractive index was established, the frequency-dependent refractive index could be obtained by normalizing to the mean value, and is shown in Fig. 8 . The absorption (loss) curve can similarly be normalized and is also shown in Fig. 8.
Fig. 8 Ordinary loss coefficient and refractive index of HOPBN. Dotted line denotes a fit to Eq. (3); the Ai coefficients are listed in Table 2.
It is seen that loss in these samples of HOPBN is an order of magnitude larger than in PBN. This may be ascribed to the layered structure of HOPBN which causes increased scattering from interfaces between the layers. Although PBN also has layered structure, it is on a microscopic scale, with layer thicknesses of 1-2 μm. HOPBN, in contrast, has mica-like structure with layers tens of microns thick. Moreover, the variable density of the samples indicates the presence of air gaps between the mica-like layers, which would contribute strongly to scattering loss. As in the case of PBN, the loss data was fitted to the Eq. (3), and the coefficients listed in Table 2. Here also, the loss is dominated by the linear component, indicating the presence of grating-like scattering at inter-layer boundaries, whilst the strong contribution from the forth-power component indicates Rayleigh scattering.
However, it may be expected that a thin film of single-layer crystalline HOPBN, which can be deposited on a variety of substrates [11], would have high THz transparency. Such films could be used as THz anti-reflection coatings if their thickness is engineered to be λ/4 of the center wavelength of the target band, which for most THz applications would be ~50 μm. Compared with metallic anti-reflection coatings [16,17], single-layer HOPBN would have the advantage of negligible loss; moreover, it would not require sub-nanometer thickness control.
5. Pressed BN powder
The loss coefficient and refractive index of pressed BN powder are presented in Fig. 9 . Also shown (dotted line) is the refractive index adjusted for porosity, calculated from the density values ρ = 2.18 g/cm3 and ρporous = 1.92 g/cm3, using the formula:
Fig. 9 Loss coefficient and refractive index of compressed BN powder. Dotted line denotes a fit to Eq. (3); the Ai coefficients are listed in Table 2.
It is seen that the porosity-adjusted refractive index of pressed powder is similar to that of the ordinary refractive index of PBN. That requires that the BN grains in the pressed powder be all aligned with their c-axis parallel to the compression axis. The grains of the BN powder are in fact better described as “flakes”, i.e. they are flat with a mean diameter of 45 μm which is much larger than their thickness of ~2.5 μm [8,10]. Each flake grows as a single crystal with its c-axis transverse to the plane of the flake. A micrograph of a pressed powder tablet presented in Fig. 10 confirms that these flakes are indeed stacked flat. The interference colors within flakes show that the flakes are optically transparent, as expected in a single-crystal.
Fig. 10 Micrograph of a pressed BN powder tablet showing the flat stacking of BN flakes. Interference colours within the flakes indicate optical transparency consistent with single-crystal structure.
The loss in pressed BN powder is notable by being much higher than in other types of BN materials, and may be attributed to scattering. Since individual flakes are comprised of fully dense BN, scattering arises from reflections at flake boundaries. A fit to Eq. (3) shows that scattering is dominated by the quadratic component. This is consistent with the known average size of the flakes which is 45 μm.
6. Conclusion
Pyrolytic boron nitride (PBN), highly oriented pyrolytic boron nitride (HOPBN), hot-pressed boron nitride and pressed boron nitride powder were examined and compared using terahertz time-domain spectroscopy. Details of the material structure, such as crystalline orientation, were derived from THz transmission properties. The value of the ordinary refractive index served to confirm that PBN, HOPBN and BN powder all have highly oriented structure; and was also used to indicate the mean degree of misalignment of the hot-pressed BN. C-cut PBN was shown to be a good candidate material for THz optics; while HOPBN, if deposited as thin films, is a candidate for THz anti-reflection coatings.
Acknowledgments
The work and NPL was supported by the National Measurement Office, an Executive Agency of the UK Department for Business, Innovation and Skills.
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